Abstract
We analyze the problem of international responsibility sharing for a refugee group seeking protection from the dangers of mass violence arising from inter-state conflict or the collapse of a fragile state. After reviewing several proposed solutions, we characterize responsibility sharing as a coordination problem in a simple sequential “moves” game between two potential host countries. We demonstrate that, ultimately, the country that makes the first move to receive refugees bears a disproportionate responsibility. We then draw on two historical case studies that illustrate the difficulties of coordinating a fair division of refugee responsibilities. To solve the coordination problem, we adapt a fair division procedure by inverting one first presented by Hugo Steinhaus for dividing “goods.” We demonstrate that the procedure is applicable to costly “obligations” under different scenarios and is manipulation proof, as each participating country has an obviously dominant strategy.
“When the drafters of the United Nations’ 1951 Convention Relating to the Status of Refugees mentioned in the document’s preamble the importance of ‘international cooperation’ in sharing the burdens created by refugee influxes, they could not possibly have foreseen the magnitude that challenge would present to refugee scholars and practitioners over the ensuing decades.” (Cook 2004, 334)
Introduction
Refugee responsibility sharing is a perennial challenge for the international community. When countries see a crisis developing, they are reluctant to offer protection because it raises the spectre of substantial costs and the fear of taking on more than their “fair” share of the burden. Nonetheless, the vast suffering of refugees and the failure of the international community to relieve it cry out for more imaginative thinking on potential solutions.
More than two decades ago, Schuck (1994, 1997) proposed an innovative solution: arrange for some international agency to assign refugee protection quotas proportionally to participating states—with the total number of quotas based on its assessment of world refugee needs—but permit them to pay other states to fulfill their obligations. His solution would have created a market for trading refugee quotas (i.e., responsibilities) and allowed the market to find an efficient allocation of them. Schuck (1997) noted that the U.S. Clean Air Act contained a related solution for environmental protection—trading emission permits. 1 Solutions with some similarities were proposed by Hathaway and Neve (1997) and Betts (2003).
These proposals raised concerns and elicited criticism from several directions. Anker et al. (1998) questioned whether countries in either the global North or South would honor their obligations to refugees under the incentives created by Shuck’s proposal. In addition, they argued that bargaining over refugee obligations would tend to weaken the norm of non-refoulement—not forcing refugees to return to face a well-founded fear of persecution—and lead to refugees being treated like commodities. Smith (2004, 149) says that, “The market for refugee quotas is simply repugnant,” and likens it to wealthy parents hiring a mercenary to take their son’s place in a universal military draft. He argues that even “debating the concept debases one of the supreme accomplishments of international diplomacy,” referring to the 1951 UN Refugee Convention. Smith’s criticism places the proposals by Shuck and others among situations in which repugnance acts as a constraint on the use of markets (Roth 2007).
Another possible solution for refugee burden sharing is two-sided matching (Roth and Sotomayor 1992), which has improved the matches of new medical doctors with residency programs, students with schools, and patients with donor kidneys (Roth 2015). The mechanisms designed to find these matches have generated solutions where market transactions fail or are repugnant to people (e.g., the sale of human organs). Several attempts have been made recently to apply similar matching mechanisms to refugees and host countries (Fernández-Huertas Moraga and Rapoport 2014; Fernández-Huerta Moraga and Rapoport 2015a, 2015b; Jones and Teytelboym 2017).
This approach is intriguing, but it has some limitations that leave room for another approach. First, it should be noted that it differs from the earlier applications of two-sided matching in that, without subsidies, the potential hosts may be reluctant to accept refugees. In some cases, the electoral consequences of absorbing refugees may concern host-country politicians even more than the financial costs. It should also be noted that moral philosophers have reservations about whether there is a moral mandate to give refugees a choice in their placement (Blake 2016, 16): If what you have a right to is a country in which your rights are respected, does it follow that you must also have a choice of which country it will be in which your rights are respected? I am not convinced that this does, in fact, follow ... [emphasis in original]
Second, and more important, when the time for action is short, information about the preferences of refugees may be far more limited than matching mechanisms require, creating practical challenges of implementation. 2 Third, this approach requires participating countries to trust outcomes generated by a centralized and rather complex mechanism. We believe there is still a need for an approach that: (1) can assure participating countries that they will not bear more than their fair share of the total responsibility, (2) makes minimal information demands, and (3) uses a decentralized and non-manipulable mechanism that is transparent to the participants. 3 The third of these desiderata is critical for the allocation process to credibly ensure the first, while preserving the active involvement of each country.
Decentralization gives each country an active role in determining the specific allocation of refugees, allowing each to make its own choices using idiosyncratic information that cannot be known ex ante to any centrally controlled procedure in a crisis situation, while still satisfying the constraint established by prior negotiations over each country’s “fair” share of the common costs of accepting refugees with different characteristics. Further, any “non-manipulable procedure” is one that cannot be “gamed,” that is, “strategy-proof.” Each participant has an obviously dominant strategy (see the Supplementary Appendix) so there is nothing to be gained by altering (manipulating) one’s choices or from knowing the others’ information and/or strategies. Any attempt to manipulate the procedure results in outcomes no better than those from choices conforming to (revealing) the country’s true preferences. Hence, non-manipulability means that each country can do no better than to follow that obvious dominant strategy.
With no international entity having the power to enforce agreements, cooperation must emerge from countries acting in their own interests. 4 We illustrate the incentive problem facing countries that find themselves in a refugee responsibility sharing situation with an ordinal coordination game. Their payoffs only reflect a rank ordering of the consequences of strategic choices, rather than any comparable values reflecting the desirability and intensity of those consequences. This enables analysis without having to know the fine details of actor preferences and beliefs, information often not available to analysts or policy makers. When we analyze this situation in the Willson (1998) version of the Theory of Moves (ToM), it becomes clear that the first mover will bear a larger share of responsibility for the refugees. Thus, countries will be hesitant to make the first move.
To further illustrate the challenges of coordination and fair division in refugee responsibility sharing, we review two important historical refugee situations. The first emerged in Europe after World War II, when the international community organized resettlement programs for more than 1 million refugees. It took place prior the creation of the current framework for refugee protection and assistance—established in 1951—and with no mechanism for a fair division of refugee responsibilities, allowing us to see what happens in the absence of such a mechanism. The second situation is the 2015 European refugee crisis—the largest influx of asylum seekers ever experienced by the European Union (EU). It took place in the same region as the first situation, but occurred when the current international refugee regime was well established. It involved negotiations for a fair division of refugee responsibilities, which ultimately failed, providing further insight into the difficulties of achieving refugee responsibility sharing.
The topic of fair division has a long history that has engaged both mathematicians and social scientists. Within the last 50 years, a few fair division procedures have been adapted to obligations (Brams and Taylor 1996), where participants seek to minimize, rather than maximize, their share. This paper adapts a procedure, first presented by Steinhaus (1948) as a way to divide goods. The procedure itself and its adaptation to obligations are not new, but its application to refugee responsibility sharing is novel. It has four attractive features for this purpose: it (1) imposes minimal information requirements, (2) is non-manipulable and transparent to all the participants in the agreement, (3) respects the independence (agency) of the participating countries, and (4) ensures a proportional allocation of responsibilities among the participating countries (in terms of people or costs, adjusted for differences in capacity to absorb refugees). We also provide a fully elaborated, formal proof of its non-manipulability in generating an equitable (proportional) allocation of responsibilities.
The next section characterizes the problem of refugee responsibility sharing as a coordination game and discusses the important historical cases noted above where responsibility sharing was problematic. The Fair Division of Refugee Responsibilities section argues that this fair division procedure guarantees a proportional sharing of refugees, or refugee costs if these differ across refugees, among N host countries, which can differ in their capacity (measured by GDP, population, or territory) to take on refugees. The Conclusion section presents our conclusions and points to possibilities for future research. All mathematical formalizations and proofs are contained in the Supplementary (on-line) Appendix.
Problems in Refugee Responsibility Sharing
A Coordination Problem
Consider three countries, labeled P, Q, and R, where Q is the country of origin for the refugees, P is a poor country near Q, and R is a rich country located farther from Q. Suppose P and R each make a choice between two policies: admit refugees from Q or not. These two choices can result in the four possible outcomes shown by the cells in the payoff table in Figure 1, where R chooses the row and P chooses the column. We represent the preferences of the countries by rank orderings of the possible outcomes or “states of play” in the cells, with the ordinal payoff for R given first and that for P given second. Higher payoffs indicate more preferred states for that country.
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Coordination Game with the Poor Country Making the First Move. The first move by Player P is taken as given. Thereafter, the players have alternating turns to move. The player with a turn to move can change its policy (move) or maintain its policy (pass). The game ends after two consecutive passes (agreement) or after four total moves (time expires).
The placement of the two highest payoffs (4) in Figure 1 indicates that each country most prefers that the other country take responsibility for the refugees. Each country also prefers to share the responsibility (3) rather than carry it alone (2). Imagine further that an intolerable situation develops (public outrage over a humanitarian catastrophe, as with the boat people in the Indochinese crisis, or loss of public support for a war, as in the Kosovo refugee crisis) if neither country admits the refugees, so that outcome has the lowest payoff (1) for each country. 6 To analyze the choices of the players in Figure 1, we must specify the rules of play for the game.
As Zeager et al. (2013) have demonstrated, the rules of play in the version of ToM proposed by Willson (1998) are useful for understanding strategic interaction among countries in a number of refugee crises. This version of ToM analyzes strategic “moves” (policy changes) in a two-player game in which both the initial “state” (pair of policy choices) and first move are treated as given by the history of the situation. The natural initial state in a refugee situation would be the one in which neither country admits the refugees. In most situations, the country in closest proximity to the country of origin—usually a poor country—makes the first move by admitting some refugees. By the time most refugee situations become international crises, things have already reached this point.
We analyze the subsequent choices of the players using the extensive-form game associated with the payoff table in Figure 1. To construct the game tree, we interpret the payoff table as a game board. The cells represent all possible states of play. The bottom-right cell (σ1) is the initial state. From that state, the row player can change the row or the column player can change the column, either of which moves the game to a new state. For example, an initial move by country P takes play to state σ2. Assume further that the players have strictly alternating turns to move, and that a player with a turn to move can either “pass” (the state of play does not change) or “move.” Thus, if country R passes after country P makes the initial move, country P can reverse its initial move (close its border), returning play to the initial state.
The game ends after two consecutive passes (indicating that both players agree to remain at that state) or when the total number of moves—not counting passes—reaches a finite limit. In the eight cases of refugee negotiations considered in Zeager et al. (2013), four total moves were sufficient to represent the sequence of moves by the players along the equilibrium path. Willson (1998) reports that for the payoff configuration in this paper, the ultimate outcome (UO) of play is independent of the total number of moves, beyond a low threshold, so the limit we impose on the total number of moves (representing the length of time available to avert a catastrophe) is not crucial to the analysis.
Given the initial state (σ1) and the first mover (P), we can use backward induction to analyze the subsequent moves by the two countries in the game tree. In Figure 1, the maximum number of moves (not counting “passes”) is four, though the UO would be the same if we allowed more moves. The game can also end after fewer moves if there are two consecutive passes. As the game is finite, we start at the terminal nodes and reason back to the initial node. At each decision node along the way, the choice (move or pass) that leads ultimately—through the subsequent moves, if any—to the more preferred state for the player making the decision is indicated by a bold arrow. If both choices lead (ultimately) to the same state, then both arrows are bold.
We can find the UO of the game by tracing the continuous path of bold arrows from the initial node to a terminal node, or perhaps more than one, each leading to the same final state when the UO is unique. In the Figure 1 game, the UO is the state σ2, which can be reached by two equilibrium paths: one involving only the initial move followed by two consecutive passes and the other involving three moves, all made by country P. On the longer path, P explores different policy options but ultimately agrees to remain at state σ2. If we enlarged the game tree by allowing more moves, other equilibrium paths would emerge but they would all lead to the same UO (σ2). This UO resembles many actual refugee situations: a disproportionate share of the responsibility for the refugees falls on a poor country near the country of origin—the source of the conflict or crisis (Betts et al. 2017). It also illustrates the situation feared by Greece and Italy, the natural entry points for geographical reasons for the Syrian refugees in the 2015 EU refugee crisis that we take up below.
We would have a different game, and obtain a different UO, if country R made the first move instead of Country P. Suppose that country P refused to grant asylum when the refugees arrived at its borders, and that some of the refugees made the longer journey to country R and were granted asylum there. This initial move by country R takes play to state σ4 in Figure 2. From there, the players have sequential turns to move and have the same options as before. Applying backward induction in that game, we find that σ4 is the UO. This UO illustrates the situation feared by Germany and Sweden in the 2015 EU refugee crisis. Hence, the country that makes the first move bears the full burden of refugee protection. It is clear then why each country is reluctant to make the first move in a refugee crisis, yet that reluctance puts the refugees at great risk. Our proposal for refugee burden sharing aims to resolve this dilemma. Coordination Game with the Rich Country Making the First Move. The first move by Player R is taken as given. Thereafter, the players have alternating turns to move. The player with a turn to move can change its policy (move) or maintain its policy (pass). The game ends after two consecutive passes (agreement) or after four total moves (time expires).
Learning from History
Having offered a game-theoretic analysis of the difficulties of coordinating a fair division of refugee responsibilities, this section illustrates the difficulties in a brief review of historical precedents.
European Refugees after World War II
When World War II ended in 1945 there were more than 11 million non-German displaced persons in the territories of Austria, Germany, and Italy (Carlin 1982). Finding places to keep them was a challenge, with much of the physical infrastructure destroyed by the war. About 8 million of these refugees returned to their countries of origin after the hostilities, including many sent back to the East against their wishes. The UN General Assembly created the International Refugee Organization (IRO) in 1946 to organize resettlement programs and it resettled more than 1 million persons in other countries by 1951. Holborn (1956) claims that the effort was, until that time, the largest organized resettlement in foreign countries of uprooted people in history.
Western countries had some reluctance to admit the refugees initially, as it was not clear to them that their labor markets could absorb even their returning soldiers, but that fear dissipated as their economies rebounded. The IRO employed three approaches to placing refugees: (1) government selection schemes, (2) transfers sponsored by voluntary societies in the resettlement countries, and (3) direct placement of individuals with prospective employers (Holborn 1956). Here we focus on the first approach because it involved the largest number of refugees and would have been a suitable context for applying a fair division procedure. The government selection process was handled by special missions sent to the occupied zones. Prior to the arrival of one of the missions (Holborn 1956, 372), “Each receiving country supplied the IRO’s central administration with particulars of the numbers of refugees it could absorb, normally classified by professions and skills as well as according to age and sex.”
The IRO did extensive preparation to place suitable refugees before the selection missions from each country. In addition to matching the profiles supplied by the potential resettlement countries with the caseloads at the various refugee centers, the IRO prepared the documentation of backgrounds, skills, and medical conditions of the refugees. In the process, it also informed the refugees of the living conditions in the potential receiving country. As things evolved, selection missions from different countries often arrived at the same time, forcing the IRO to use larger centers for resettlement selection. Members of the selection missions usually reviewed the documents prepared by the IRO before interviewing the refugees. The interview process varied from one country to another, but the account of the Australian approach is particularly apt to our proposal presented below (Holborn 1956, 373): With documents and the refugee family in front of him, he was able, with the help of the field resettlement officer, to select the sort of family his government wanted. Often the family composition didn’t fit into the pattern of the selection criteria. There were grandparents who were too old, or there were too many members in the family, or the ratio of workers to dependents did not satisfy the precise requirements of the agreement. However, if the family appealed to him, if he felt that here was the type of future citizen that Australia needed, he would send the whole group on for processing.
As the participants gained experience they learned that (Holborn 1956, 376): ... agreements were best limited to questions of policy, such as numbers, age limits, family composition (the general proportion of workers to dependents), medical standards, conditions of work, rights and duties of the immigrants, respective responsibilities of the contracting parties for transportation both overseas and inland, conditions for admission of workers’ dependents, and conditions under which undesirable immigrants could be returned to their country of origin. … there were as many different types of schemes as there were countries.
In these descriptions, we see each country proposing to resettle some portion of a heterogeneous refugee population, with the country representative making an assessment of the cost associated with its proposed portion. We also see the country exiting the process after receiving its portion.
What is missing from these accounts is any cooperation agreement among the host countries or any mutual consideration of the “fairness” of the shares of refugees taken by the different country missions. Instead of a review by the other countries involved in the resettlement—which will play a central role in our proposed solution to the coordination problem—separate negotiations were conducted between the IRO (representing the refugees) and individual countries. (Holborn 1956, 370) reports that, “It [the IRO] continuously exerted all its influence to persuade reception countries to enlarge their resettlement criteria… ”. Given that different countries were choosing at the same time and place, it would have been possible for the selection missions, rather than the IRO, to review the proposals by other countries and offer to enlarge those that were less than a fair share in their estimation. Of course, such an arrangement would have required a major cooperation agreement among the participating parties.
We can obtain one measure of the allocation of refugees by the actual process from Loescher (1993, 52): During the four and one-half years of IRO operations, the United States received 31.7 percent of the refugees resettled; Australia 17.5; Israel 12.7; Canada 11.9; Britain 8.3; Western Europe 6.8; and the countries of Latin America 6.5.
In terms of numbers of refugees, the United States admitted about 400,000. It also contributed over $250 million toward the more than $400 million of total expenditures by the IRO during its 4.5 years of operation (Loescher 1993). While the overall operation was unprecedented in size, roughly 1.25 million more refugees remained unsettled (Carlin 1982), or about one-half the refugee population needing a permanent place to go. The IRO saw patterns of discrimination emerge against Jews, intellectuals, and especially aged, sick, and handicapped persons. The most difficult of these cases came to be known as the “hard core” group, totaling about 400,000 people, comparable to the total number of World War II refugees admitted by the United States to that point (Loescher 1993).
There was no requirement in this case for the host countries to collectively absorb all of the refugees, as there was a surplus of them after all the countries took their portions. This group became the greatest burden-sharing challenge in WW II resettlement. According to Loescher (1993, 52), “The scandal of these camps was to become a subject of criticism in the West and elsewhere for the next 10 years or more.” It also illustrates the problem with allowing the countries to “skim the cream” of the refugee population, which the procedure we propose is designed to prevent.
The inability to find a resolution to the post-war refugee problems led to disenchantment with the IRO in the U.S.—its main benefactor. The U.S. began to pursue alternative strategies, culminating in the Marshall Plan, designed to stimulate economic recovery in Europe and make it easier to absorb the refugees there. To replace the IRO, the U.S. initiated discussions to create a new refugee organization, the United Nations High Commissioner for Refugees (UNHCR), to deal with new flows of refugees created by the increasing tensions between the East and West (Loescher 1993).
We believe that this case, while relatively “successful” by historical standards, shows the need for a cooperation agreement among countries on a fair division procedure for refugee responsibility sharing. Given that participation in this arrangement was voluntary, it was welfare improving for the host countries. However, it was only a partial solution, as it left a very large and difficult problem behind. It also provides a cautionary tale about what can happen when proposals for taking portions of a refugee population are negotiated separately by each country with a humanitarian agency (UNHCR, for example), without a mechanism to ensure a fair allocation of responsibilities such as we propose below.
The 2015 European Refugee Crisis
Despite substantial progress in the development of international institutions and policies to deal with refugee crises, the issue of fairly allocating responsibilities remains problematic. This can be seen in the recent refugee crisis in Europe, one that took place after the current refugee regime—the 1951 Convention and the 1967 Protocol—were well established. It involved 28 EU Member States and a few other countries, which represents in microcosm a situation roughly comparable to the global refugee challenge: richer and poorer potential host countries, with the latter closer (by land or sea) to the main refugee source countries.
The number of asylum seekers in the EU, Norway, and Switzerland surged to 1.325 million in 2015, more than double the combined influx from the previous peak years of 1992, following the fall of the Berlin Wall, and 2002, in the aftermath of the war in Kosovo (Pew Research Center August 2016). The largest shares of asylum seekers came from Syria, Afghanistan, Iraq, and the Balkan states, though the last group had much lower acceptance rates (Aiyar et al. 2016).
By official policy within the EU, “Under the Common European Asylum System, to prevent multiple applications, the first country where the asylum seeker is registered is responsible for processing the asylum application, with a few exceptions such as family cases ...” (Aiyar et al. 2016, 11). Greece and Italy were the attractive landing points for those coming by sea; however, both countries were known to allow asylum seekers to pass through their territories in violation of the official policy. The proximity of Hungary to Turkey—a neighbor to both Syria and Iraq and host to more than 2 million displaced persons—made it the most attractive entry point by land. Germany and Sweden were also appealing due to their prosperity. For all these reasons, asylum applications were unevenly distributed across the European countries; per 100,000 in population, the numbers ranged from over 1500 in Hungary and Sweden to under 150 in Italy, France, Greece, Ireland, and the United Kingdom (Pew Research Center August 2016).
Given the disregard of official policies by the perimeter countries and the uneven distribution of asylum applications across countries, it is not surprising that European public opinion surveys registered high rates of dissatisfaction with the handling of the crisis. Growing political pressures, leading to gains by anti-immigration parties, prompted negotiations among the EU countries and led ultimately to an announcement by the European Commission (EC) on 9 September 2015 of a comprehensive package of proposals (European Commission 2015, 1): The new set of measures will alleviate pressure from Member States most affected - notably
These proposals were not intended only for the crisis at hand (European Commission 2015, 1): As announced in the European Agenda on Migration, the Commission is proposing a structured solidarity mechanism which can be triggered any time by the Commission to help any EU-Member State experiencing a crisis situation and extreme pressure on its asylum system as a result of a large and disproportionate inflow of third country nationals.
The Commission’s proposals included a refugee quota system with a “distribution key” (determining the number of asylum seekers allocated to each Member State) that depends on four factors: population size (40%), GDP (40%), an average of the number of asylum applications received over the last 4 years (10%), and the unemployment rate (10%). Based on an analysis of national surveys, EU documents, press reports, and interviews with experts, Zaun (2018) finds that a permanent distribution key appealed to the main host countries in the 2015 crisis (Germany, Austria, and Sweden), others who often had high asylum application rates (the BENELUX countries—Belgium, the Netherlands, and Luxembourg) and border countries with heavy transit flows (Italy, Greece, and Slovenia), but not at all to the Visegrad States (Czechoslovakia, Hungary, and Poland), the Baltic States (Estonia, Latvia, and Lithuania), and Spain. The resistance was based on concerns that binding quotas would violate state sovereignty, might encourage additional asylum seekers to come, and could not ensure that those allocated to a country would stay where they were placed. The Czech Republic, Hungary, Romania, and Slovakia voted against the proposal and Hungary was later removed from it (Bovens and Bartsch 2015).
On the issue of temporary refugee quotas, however, there was more flexibility in the negotiations. Zaun (2018, 55) reports that: Despite this lack of enthusiasm for the proposal, Member States could still agree on the crisis relocation scheme, as it was only temporary and considered by most as a means to support the “front-line” states Greece and Italy, which had been clearly overburdened by the increased inflow of asylum-seekers ... Most Member States were simply not ready to support Germany, Austria, and Sweden to the extent that they would have supported the border countries. These states were not only wealthier and more capable of receiving refugees, but they were also accused of having further motivated asylum-seekers to come to Europe through their temporary open borders approach ...
Given widespread resistance to and noncooperation with the proposal for a permanent solution, 7 the 2015 EC proposal was eventually abandoned and replaced by a new proposal—A New Pact on Migration and Asylum (European Commission 23 September 2020).
Bovens and Bartsch (2015) fault the EC’s distribution key for allocating too many asylum seekers to poorer eastern and southern EU states. They propose an alternative distribution key based on two factors: GDP per capita and population, multiplied and equally weighted. To simplify the comparison, we drop the two small “corrective factors” in the Commission’s distribution key (prior admissions and the unemployment rate), which in this situation are not far from offsetting. 8 Let Y denote GDP and P denote population, so that GDP per capita is y = Y/P Y . Then the EC’s (simplified) distribution key is 0.5Y + 0.5P and the proposed alternative is yP (= Y). Note that in the latter, a doubling of GDP per capita combined with a halving of the population yields the same allocation, which Bovens and Bartsch (2015) call “the principle of equal proportional sacrifice.” Clearly, putting all the weight on GDP augments the allocations to the richer countries, which may have made the proposal more palatable to the poorer EU states.
The EU experience in 2015 showed that the choice of a distribution key can be an important challenge in negotiations for refugee responsibility sharing, which prompted a small literature on the factors that should be included. Bovens and Bartsch (2016) amended their proposed distribution key to include three indices of capacity to absorb refugees: GDP, the job vacancy rate, and the proportion of the population over age 65. Higher values for any of the three indices increase the allocation of asylum seekers to a country. Holtug (2016) accepted all the criteria in the EU distributive key, but then suggested additional considerations in designing a fair distributive scheme: the short- and long-term costs of providing for the refugees (e.g., social welfare benefits and educational opportunities), cultural affinity to the country’s population (e.g., language and religious background), and the potential for hostility, harassment, and violence. He also emphasized that “a distribution scheme should ... cater for all refugees with a claim to asylum” (Holtug 2016, 285), which reflects one of the main lessons from the post-World War II refugee experience discussed above.
What lessons can we glean from the 2015 European refugee crisis? First, notice that both possible outcomes of the moves game described above emerged as possibilities in this crisis. If the poorer border states nearest to the source countries for the refugees had chosen to do what the official EU asylum rules required, they would have been saddled with a disproportionate share of the responsibility. However, they anticipated that outcome and disregarded the rules, allowing asylum seekers to pass through their territory and apply in more prosperous EU Member States. This choice led to the second possible outcome, where the richer states bore a disproportionate share of the burden. Second, we see in the EU negotiations for a redistribution of asylum seekers that some countries were implacably opposed to the redistribution while others were receptive to the idea under certain circumstances. We propose a new framework for implementing responsibility sharing that alleviates several concerns that make countries on the margin reluctant to participate, thereby improving the likelihood of their inclusion.
In the next section, we present a mechanism for the non-manipulable implementation of any distribution key that the participants agree upon. A distribution key must be the outcome of political negotiations and thus, will likely vary from case to case, so we do not specify a distribution key. We assume here that such issues have been resolved to the point where there is an accepted key to be implemented. We assume further that if one or more countries refuse to participate—like Hungary and Poland in the 2015 EU refugee crisis—the remaining participants agree to divide among themselves the fixed number of refugees in need of protection. The mechanism we propose cannot transform implacable opponents into willing participants, but it alleviates some problems that make other countries hesitant to participate and ensures that all the refugees are allocated to one of the participating countries. It can allocate either refugees or the costs of providing for them (if these differ across refugees) conditional on the distribution key chosen by the potential asylum countries.
The mechanism bestows on the participating countries an active role (i.e., agency) to respect their sovereignty—a concern that arises in efforts to achieve a fair division of refugee responsibilities and often undermines those efforts. Its operation is relatively simple and transparent to alleviate fears of manipulation and it also has modest information requirements. We believe that the mechanism is most applicable in a rapid emergency response to an ongoing crisis where there is limited time for probing into the details of refugee circumstances or country needs. Once an allocation has been made and there is time to collect more information, methods that take this additional information into consideration could be used to refine the allocation.
Fair Division of Refugee Responsibilities
We want to find a procedure that, if adopted by N host countries that agree to share responsibility for a specific refugee population of size M, would implement a fair (proportional) division of responsibilities.
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Such a procedure would remove a major concern behind the widespread reluctance to offer protection to refugees—the fear of getting stuck with a disproportionate share of the responsibility. Given the nature of international refugee negotiations, we must rule out solutions imposed by an outside party (e.g., an arbitrator), but not the assistance of a mediator—such as a representative of UNHCR—to clarify the procedure, ensure its transparency, and impartially guide its implementation for countries agreeing to use it. Before introducing the procedure, we share an observation by Blake (2016, 16) when he considered “the problem of distribution” for a group of refugees: ... people are not goods to be distributed, and still less are they burdens to be shared – but political reality demands that we recognize that sometimes they must be understood as such, for purposes of political discussion.
The literature on fair division has a long history, but we focus here on a more recent strand that extends fair division to “burdens” (household chores or civic duties such as paying taxes, performing military service, etc.), apparently first pursued by Gardner (1978) according to the most comprehensive source (Brams and Taylor 1996). 10 In such situations, some procedures that guarantee a fair division of goods—where each party seeks to maximize its share—can be inverted to yield a fair division of duties—where each party seeks to minimize its share.
Among the set of fair division procedures described in Brams and Taylor (1996), we eliminate all that lack the inversion capability, all that cannot be applied to any number of parties, those that require fine information about the preferences of the parties, and those that involve imagery that is repugnant when applied to refugee populations (e.g., “moving-knife procedures”). The most promising (i.e., simple, transparent, and practical) one that remains is the “last-diminisher” procedure proposed by Stefan Banach and Bronislaw Knaster to their former teacher, the mathematician Hugo Steinhaus, who was the first to describe their proposal in print (Steinhaus 1949, 1948). 11 We adapt this procedure, which we call the “Banach-Knaster (BK) mechanism,” to the division of refugee obligations among N countries.
We want to consider the possibilities for applying the BK mechanism to refugee situations that are unfolding, where the case for providing asylum is compelling, and the presumption is that the asylum seekers will be designated as refugees (under the 1951 Refugee Convention and 1967 Protocol) upon proper review. Without a presumption of refugee status, discussion of a fair division would be hampered by uncertainty about the size of the refugee population (M) in need of protection. Blake (2016, 4), a moral philosopher, argues that the Syrian refugees represent a situation such as we have in mind: I’m going to assume—not, I think, unfairly—that the people risking death in the flight from Syria are fleeing circumstances that are morally objectionable. In particular, I will assume that these people are fleeing institutions and practices that pay radically insufficient respect to their bodies, their lives, and their relationships with other people.
The countries engaged in bombing Kosovo in 1999 had a similar presumption about the ethnic Albanians who fled but found themselves trapped on the border with Macedonia. Those countries launched a rescue operation by airlifting the presumptive refugees to other countries for protection, called a “Humanitarian Evacuation Programme” (Williams and Zeager 2004). Carens (2013, 192) notes that “Contemporary reflection about refugees begins in the shadow of the Holocaust” and builds his case for accepting refugees on “one fundamental truth: Jews fleeing Hitler deserved protection, and most of them did not get it.” The BK procedure provides a straightforward approach to dealing with such situations.
Heterogeneous Refugees and Differing Country Capacities
The mechanism provides a decentralized procedure that implements a “fair division” of a burden—the “costs” of a commonly accepted responsibility for refugees in a crisis situation—in a transparent, non-manipulable way. It is intended to be applied at the state level, with the representatives of the cooperating countries deciding on an allocation among themselves of a mass of refugees in need of protection from life-threatening circumstances. We assume that, in the crisis, the preferences of the different countries are aligned—to share proportionally the known, direct costs of providing refuge to that mass of humanity.
A heterogeneous refugee population means that each refugee or refugee family imposes a (potentially) different burden or cost on its host country. 12 Refugees and their families are very diverse, differing by age (children, working-age adults, and the elderly), gender, education, medical condition (perhaps with injuries or deprivations suffered while living in a conflict region), etc. Women and children are usually disproportionately represented. We assume further that the costs of certain refugee characteristics—the schooling needs of children, the support of the elderly, and some basic medical care for the injured—are commonly known to the recipient countries and can be negotiated in the distribution key that provides a framework for the actual allocation procedure. Other characteristics—historical ties (social, religious, etc.) and labor market needs—are idiosyncratic, details too fine to incorporate into the distribution key; these are considerations for each country to weigh when selecting specific sets of refugees for which to bid. Some idiosyncratic details are initially unknown. After the refugees receive a basic level of protection and the finer details become known, a further stage of reallocation, matching country and refugee preferences, could be implemented. We do not believe that there is enough common information for this to be done in the throes of a crisis.
We also allow countries to have known, commonly agreed to, relative “capacities” to bear the costs of accepting refugees. In many refugee situations, countries differ in their capacities to absorb refugees due to differences in GDP, population, or geographical area. Considerations of capacity differences across host countries have been an important issue in the refugee studies literature. Czaika (2005) proposed a “refugee capacity index” for adjusting a country’s share of the total refugee population involving three equally weighted dimensions: economic (GDP), societal (population density and ethnic, linguistic, and religious fractionalization), and political-institutional (political freedom and stability). The issue arose in the EU after waves of refugees from Syria and other countries crossed its borders. Discussions among the EU countries resulted in a 2015 relocation proposal with a “distribution key” that assigns differing weights to GDP, population size, the unemployment rate, and the number of prior asylum applications (Betts et al. 2017). There was strong push-back from certain EU governments, yet there was also evidence of majority support in many of these countries for a distribution key for responsibility sharing. Bansak et al. (2017) did a survey of 18,000 citizens of 15 European countries and found that a large majority favored allocations proportional to country capacities over allocations to the country of first entry (the status quo). When a randomly assigned portion of the respondents were told that switching to proportional allocations would increase the allocation to their own country, a smaller majority were still supportive.
The BK procedure is implemented by the following algorithm, with countries ordered (1, 2, . . ., N): 1. Country 1 proposes a portion of the refugee population, and its associated costs, as its fair share. 2. Country 2 has the right—without obligation—to augment the portion, along with its costs, claimed by Country 1. 3. Whether or not Country 2 chooses to exercise this right, Country 3 has the right—without obligation—to augment the portion, and its associated costs, after the decision by Country 2 has been made. 4. The same process continues through each successive party, up to Country N. 5. The last country to augment the portion initially proposed by Country 1 is obligated to take that augmented portion, and its associated costs, and depart from the procedure. Or if no other country augments the initial proposal, Country 1 is obligated to take its proposed share of the total refugee obligation and depart. 6. The remaining N − 1 countries repeat the steps above until only two countries remain. The same procedure can be applied to the two remaining countries, and in this round it resembles the familiar divide-and-choose rule, where the first mover divides the remaining refugees (and costs) and the second mover chooses.
We will consider applications of this procedure under different assumptions about the characteristics of the refugees and the host countries, and the terms of the bids placed by countries will depend on these characteristics. When the refugees are homogeneous and country capacities are identical, bids will be for shares of the total number of refugees. When we allow costs to vary across refugees, bids will be for shares of the total costs. The mechanism does not directly incorporate idiosyncratic costs of countries for the same refugee, although it allows such differences to influence the bids of countries for sets of refugees. When costs vary across refugees and capacities differ for countries, bids will be for per-capacity-unit shares of the total costs, which allows a country with a smaller capacity to outbid a country with larger capacity if its bid is larger in per-capacity-unit terms than that of the greater capacity (larger) country, as we show in the Supplementary Appendix.
Doubts have been raised about the practical usefulness of fair division procedures, beyond the simplest ones. In his review essay on Brams and Taylor (1996), the psychologist Murnighan (1999, 154) writes, Although Brams and Taylor would like to see the procedures they have analyzed put to use, there are many reasons why this is unlikely. Many anecdotal observations suggest that people understand and are comfortable with coin flips and divide and choose. Using more than these simple, straightforward procedures, however, can lead not just to reticence but also to refusal.
Schneider and Krämer (2004) provided the first empirical test of this issue in an experimental setting, though they did not examine the BK mechanism. They found some limitations to the purported gains from more complex fair division procedures relative to the classic divide-and-choose procedure when the “rules of play” were not strictly enforced. They also reported that the advantages of the complex procedures were dependent on the psychological profile of the participant.
We believe the demands on a country in the BK procedure do not differ greatly from those in divide and choose. Indeed, the final round of the procedure is equivalent to divide and choose. In the earlier rounds, a country makes a bid when it plays the role of Country 1 in the BK procedure, which is comparable to the role of the divider in divide and choose. It also monitors the bids of other countries to ensure that no country avoids its fair share of responsibility. This activity seems no more challenging than playing the role of the chooser in divide and choose. Each bid/pass requires only a comparison of size (numbers or costs), without complicated calculations such as those required to solve any optimization problem. Moreover, once countries have agreed to the process, relatively little time and effort is required to set up and implement the process. As the iterations are all internal, only a few days would be necessary to achieve a complete allocation assignment (even if the number of countries is large) once empowered by national governments and assembled in a single location. The supervision of the multi-stage procedure can be left to a neutral mediator from the UNHCR or another international agency that specializes in the role, freeing the country representatives to focus on making and monitoring bids. Indeed, the empirical test by Schneider and Krämer (2004) suggests that strict enforcement of the rules of play would enhance the gains from using the BK mechanism.
One might ask why the BK mechanism is even necessary. If the N countries can agree on the rule for determining fair shares, why not have a centralized mechanism simply assign those responsibilities to each country? We have two responses. First, the BK mechanism gives each country active agency in the solution of the problem, which allows their preferences to influence the refugee allocation. It is important to understand that the informational and prior agreement assumptions in the model just provide a framework for the actual selection process (the BK mechanism); they do not determine any specific allocation of the refugees. The mechanism allows countries to select, subject to the “fairness” constraint (distribution key), which specific group of refugees, to the best of their (limited) knowledge, would be the least costly. The actual allocation is determined by the iterative selection of specific sets of refugees by the individual countries, which will naturally be driven by the finer “preferences” of the countries. Those countries will, in making their selections (“bids” for sets of specific refugees), take account of how their particular circumstances (culture, religion, ethnic composition, etc.) impact the ultimate burden they will bear, just as the heterogeneity of the cake affects the “cuts” made in the “cake-cutting” application of the mechanism. 13 Therefore, the procedure not only facilitates the implementation of a “fair” allocation, it enables the participating countries to discover that allocation in the process of their interaction.
Second, the BK mechanism neatly addresses a vexing concern in the existing literature, articulated vividly by Carens (2013, p. 221), ... those states that are willing to fulfil their obligations to refugees could face an endless ratcheting up of their responsibilities. [S]uppose we had a fairer allocation of responsibilities for refugees ... and then other states failed to fulfil this duty... Would the states that were willing to meet their secondary responsibilities... be obliged to take up the slack, admitting still more refugees... than required by their initial fair share, because the refugees’ moral claims to membership in some society would otherwise go unmet?
Carens (2013, 221) describes this problem as “the dynamic of cascading moral failures” and the BK procedure is specifically designed to cut that dynamic short within the group that adopts the procedure. By having the countries monitor each other, it ensures that no country escapes with less than its fair share of the responsibility and that no country is obliged to take up the slack. The practical need for such a mechanism is clear from the problems that arose in the historical cases described above. 14
We turn now to the formal analysis of the BK mechanism. Referring to the division of goods, rather than obligations, Steinhaus (1948, 102) claims that, “It is easy to prove that the methods explained here secure to every partner at least a part equal to the value of 1/Nth of the whole,” but he does not provide a proof. We adapt this claim to the division of obligations and provide the formal proof in the Supplementary Appendix. We formalize the BK procedure into a game-form and prove that it is non-manipulable by the players. The main result—Proposition 1 in the Supplementary Appendix—shows that the BK mechanism yields a fair division of responsibility in equilibrium, that is, equal (explicit and commonly recognized) costs per capacity unit across all countries.
In the Supplementary Appendix we note that the BK mechanism has the structure of an increasing-cost clock auction. It is well known that the winning bid in such auctions is (essentially) determined by the valuation of the second-highest bidder (Rasmusen 2007), so if we allowed the costs imposed by specific refugees to differ across countries, “equal costs per capacity unit” would be an upper bound on the burden each country will bear. The BK mechanism also has the property of non-manipulability because its structure resembles an increasing-cost clock auction. Implementation of the BK mechanism involves N − 1 rounds of “bidding” for a set of refugees, in an order prespecified for each round. 15 In each round, the first agent must offer to take (“bid for”) some set of refugees. Later agents in the order move sequentially and may either “bid” or “pass.” “Bids” for any set of refugees are required to be increasing in the burden relative to capacity of each country, while a “pass” moves the opportunity to bid to the next agent in the prespecified order. Once all agents involved in the round have bid, the one with the “highest” (largest) bid relative to its capacity to absorb refugees, that is, the last one to actively bid in that round, “wins” the set bid for, and then exits the procedure, leaving one fewer country bidding in the next round. If all other countries active in the round (i.e., that have not exited earlier with a subset of the refugees) pass after the first makes its mandatory bid, then that first country gets the set of refugees requested, and exits the procedure. In the N − 1 round, only 2 countries remain, so the first mover essentially “cuts” while the second chooses by “passing” if the bid is fair or excessive or ε-augmenting the bid if it is less than a fair share of costs. Note that the BK mechanism requires only (1/2)(N − 1) (N + 2) decisions by participants (“bid” or “pass”) over the (N − 1) rounds as the “winner” in each round drops out of the bidding in the following rounds.
Special Cases and Limitations
Here we consider the special case of an extreme refugee crisis where rapid action is essential to prevent a humanitarian catastrophe and there is no time to gather detailed information about the refugees beyond an estimate of the total number in need of protection. Lacking detailed information, each refugee is assumed to entail the same cost for any recipient country, so the population of refugees is treated by the countries as homogeneous. As before, countries have differing capacities to absorb the refugees. In this case, the equilibrium of the procedure is, just as before, for each country to bear the same costs per capacity unit, as formalized in Corollary 1 in the Supplementary Appendix. There we also present a counterexample to the intuitive possibility that a much larger country can grab a favorable (less burdensome) allocation of responsibility, illustrating the non-manipulability of the mechanism.
A simpler case arises when, as in the previous case, rapid action is essential to prevent a massive humanitarian disaster and detailed specific information about the refugees is unavailable—other than an estimate of the total number of refugees needing protection—but the number of refugees is sufficiently small that capacity constraints are not an issue for any of the participating countries. We show that in this case the equilibrium of the procedure is simply equal allocations of the refugees among countries, regardless of the unknown specific costs, as formalized in Corollary 2 in the Supplementary Appendix.
This case is simple enough to provide a graphical illustration that gives an intuitive feel for the BK mechanism. Figure 3 illustrates the BK allocation mechanism in Corollary 2 with N = 3 host countries.
16
In round 1 of Figure 3, Country 1 proposes taking a share (s1) of M total refugees. We aggregate the options available to Country 1 into three categories: less than a fair share, a fair share (1/3), and more than a fair share. If Country 1 chooses the middle category, neither Country 2 nor Country 3 will augment the proposed share, so Country 1 would take its fair share and leave. Then Country 2 and Country 3 would be left with MN−1 = (2/3) MN−2 refugees to divide in the final round. Notice that the final round is essentially like the familiar divide-and-choose method, with Country 2 proposing the division. By backward induction, the optimal choice for Country 2 is to propose a fair share (s2 = 1/2) of the remaining refugees and the optimal choice for Country 3 is to pass. Banach-Knaster Refugee Allocation Mechanism with Homogeneous Refugees and Three Host Countries. Note: Each country seeks to minimize its share of the refugees. In Round 2, (1-Sout) M refugees remain. We illustrate the remainder of the game tree for only one possible node at the beginning of Round 2 (the one on the equilibrium path). The tree structure at the other nodes would be similar and would result in the payoffs shown in place of those portions of the tree.
Space does not permit us to illustrate the full three-player game tree with all round 2 subgames laid out, but round 2, with 1 less agent, has the same structure at every node (subgame). Thus, using the module that is illustrated and noting which pair of countries remain at each node, we can determine the payoffs that each country will receive if they reach any node at the end of round 1. For the case in which Country 1 proposes less than a fair share in round 1, Country 2 would augment the proposal to s2 = 1/2; otherwise, Country 3 would escape with a share strictly between s1 and 1/3. After Country 2 augments the proposal by Country 1, Country 3 would pass to end round 1. Looking at the payoffs associated with this node, we can see that this side of the game tree leads to the same UO as the middle part of the tree—a proportional division among the three countries.
In the event that Country 1 proposes taking more than a fair share of the responsibility, the other two countries would both pass, forcing Country 1 to leave with more than a fair share. Countries 2 and 3 then receive a less than fair share after dividing the remaining refugees. But by backward induction, Country 1 would not choose the branch leading to this side of the tree. Thus, there are two possible equilibrium paths in Figure 3, with both paths leading to a fair (proportional) division of the refugees (s1 = s2 = s3 = 1/3).
The final corollary addresses the remaining case in which more detailed information is available on the refugees, but the total number is sufficiently small that capacity constraints are not an issue for any of the participating countries. In this case, there are clear, accepted, and possibly different costs associated with each set of refugees. We show that, in equilibrium, there will be equal costs per country, as formalized in Corollary 3 in the Supplementary Appendix. Corollaries 2 and 3 together show how the form taken by the equilibrium of the BK procedure (equal numbers of refugees or equal costs per country) depends on the source of the heterogeneity (refugees or countries).
It is worth emphasizing what Proposition 1, Corollaries 1 through 3, and their proofs do and do not do. They apply a known “cake-cutting” procedure to the inverted problem of dividing a burden rather than a “good,” and show in that case that a simple, decentralized procedure can provide an incentive-compatible mechanism capable of achieving, through (N − 1) sequentially nested “auctions,” a fair (proportional) allocation of the burden. We do not address issues of the computational efficiency of the mechanism, its optimality, or even the envy-freeness of the resulting allocation, but only the one-dimensional issue of basic “fairness”—a proportional allocation of the costs of accepting responsibility for the refugees. The focus is on the simplicity and straightforwardness of the mechanism, one where it is obvious that attempting to “game” the procedure can only lead to a no better, and perhaps worse, outcome.
The results depend in part on assumptions limiting the preferences of the agents that are derived from our understanding of refugee crisis situations. First, in the throes of a looming humanitarian disaster, the detailed preferences of the refugees are irrelevant; their immediate need for protection dominates any preferences over paths and destinations. This mechanism is not used to make complete “life choices” for refugees, but just to organize temporary “protection” in the unfolding crisis. Second, the mechanism limits the range of recipient country preferences, assuming that they only care about the relative size of the burden, measured in the relative costs of accepting responsibility for some number of refugees. Thus, the heterogeneity of refugees is only reflected in differences in the cost of protecting them. This essentially assumes that, in responding to the immediate crisis, the preferences of the cooperating countries are aligned—rescuing all the refugees through a fair allocation of commonly recognized (per unit capacity) costs—allowing clear, transparent inter-country comparisons. Of course, in choosing sets of refugees to accept, a country will take account of idiosyncratic cost details that are not explicitly incorporated into the mechanism framework.
Regarding the first point, it is hard to believe that the informational prerequisites for various matching procedures—which rest on the elicitation of preferences dependent on the fine characteristics of the parties involved—could be met in a true refugee crisis situation. Once initial placement (the objective of the BK mechanism) has removed the immediate danger, the refugees could be allowed to enter into a “reallocation” matching process, where both the finer preferences of countries over refugee characteristics and of the refugees over destinations should be taken into account; that involves analysis beyond the scope of this paper. We believe that similar problems arise with respect to the recently proposed use of tradable quotas, which are essentially a “Coasian” alternative to using a market-like mechanism with Pigovian taxes/subsidies to allocate the burden, relying on ex post-trading of refugee quotas to “correct” the initial inequitable allocation. Thus, it seems best to think of the BK mechanism and the market mechanisms as tools for different situations, with the BK mechanism being more suitable for crisis situations in which time and information are very limited.
Conclusion
Our aim in this paper has been to find a relatively simple, transparent mechanism for allocating a group of refugees fairly among a set of countries that are willing to provide protection for them. Having such a mechanism in place would mitigate a major source of reluctance to act in these situations and allow a more timely response. As we have shown, without a fair division mechanism, the potential host countries face the payoffs of a sequential-move coordination game, where the one that makes the first move to admit refugees gets a disproportionate share of them. Thus, each country fears the risk of bearing more than its fair share of the responsibility, and this fear can lead to hesitation with potentially tragic consequences.
Two important historical cases illustrate problems that can arise in refugee responsibility sharing. In the resettlement operation for post-World War II refugees in Europe, no fair division mechanism was used. Each host country negotiated separately with the humanitarian agency responsible for the refugees, allowing the host countries to “skim the cream” of the refugee population—healthy people of working age with skills that were useful in the host country—leaving an unclaimed residual of the aged, sick, handicapped, and others facing various forms of discrimination. In the 2015 European refugee crisis, the rules for asylum applications would have saddled the poorer EU countries nearest to Syria and Iraq with a disproportionate share of responsibility, as implied by our sequential-move coordination game. When these countries ignored the rules and allowed asylum seekers to pass through their territories to richer EU countries, the latter were unable to convince enough EU Member States to redistribute the refugees more evenly. As in our sequential-move coordination game, if a country makes the initial move to accept the refugees, it bears a disproportionate share of the burden.
We identify a procedure for implementing responsibility sharing that leaves no residual of unclaimed refugees and mitigates concerns that can undermine efforts to achieve a fair allocation of obligations, making it more attractive to countries that are open to being persuaded to participate. We demonstrate that the procedure—the BK “last-diminisher” procedure for allocating “goods” among N parties described in Steinhaus (1949, 1948)—when inverted to deal with obligations, provides a non-manipulable mechanism [i.e., obviously strategy proof (Li 2017)] for making a proportional allocation of a refugee population among N host countries. It respects independence and sovereignty by giving each country agency through bidding for an allocation of responsibilities and monitoring the bids of others. It is simple and transparent to alleviate fears of manipulation and has modest information requirements. The BK mechanism is flexible; it can work with either small or large numbers of host countries and any distribution key they agree upon. The mechanism can also accommodate heterogeneity within the refugee population (by making a proportional allocation of costs rather than persons) and differing capacities (GDP, population, or territory) among the host countries. It does not require centralized control, only a cooperation agreement among the host countries to adopt and adhere to the simple procedure. By making the host countries active participants in the BK allocation procedure—where choices are informed by their own preferences—each country can come out feeling that it has done better than under any arbitrary allocation imposed by the distribution key, while still conforming to its constraints.
We have focused on the responsibility of countries to provide basic protection to refugees on the run, where information on the refugees is very limited, rather than on the long-term issue of finding the best permanent matches between refugees and countries. We believe the properties of the BK mechanism make the procedure practical to use for refugee crises in which a group of countries wants to allocate the influx in a way that guarantees that no member will receive more than its “fair” share of the refugees.
We leave several important issues for future research: scalability to very large numbers of refugees, differences in idiosyncratic costs among countries or, more generally, in country preferences with regard to different types of refugees, including the possibility of refugees being considered “mixed manna” (Bogomolnaia et al. 2017)—where the population contains persons (young, healthy, highly skilled) who are, from the point of view of some or all of the host countries, a net benefit, as well as others who are a net cost—and finally incorporating refugee preferences for locating in different countries. With regard to differences in preferences among countries and refugees, we note that, once the refugees have received basic protection and detailed information about them can be collected, a centralized two-sided matching or market mechanism could be used to improve the matches, for example, Fernández-Huertas Moraga and Rapoport (2014) or Jones and Teytelboym (2017). Likewise, after the BK allocation of refugees among the countries, methods for matching the refugees to locations within any country based on integration outcomes—determined by data-driven machine learning methods (Bansak et al. 2018)—and even basic information on refugee preferences over these locations (Acharya et al. 2021) could be employed.
Supplemental Material
sj-pdf-1-jcr-10.1177_00220027221080985 Supplemental Material for Coordination and Fair Division in Refugee Responsibility Sharing
Supplemental Material, sj-pdf-1-jcr-10.1177_00220027221080985 for Coordination and Fair Division in Refugee Responsibility Sharing by Richard E Ericson and Lester A Zeager in Journal of Conflict Resolution
Footnotes
Acknowledgements
We thank Alexander Betts, Steven Brams, Eugene Eisenstein, Paul Huth, Alvin Roth, and two anonymous referees for valuable comments. Kasra Khademorezaian provided excellent technical assistance with LaTeX. We are responsible for any remaining errors.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.
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References
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